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Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
This paper proposes a novel non-autoregressive (NAR) block-based Attention Mask Decoder (AMD) that flexibly balances performance-efficiency trade-offs for Conformer ASR systems. AMD performs parallel NAR inference within contiguous blocks…
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in…
Distributed optimization is an essential paradigm to solve large-scale optimization problems in modern applications where big-data and high-dimensionality creates a computational bottleneck. Distributed optimization algorithms that exhibit…
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…
We provide effective algorithms for solving block tridiagonal block Toeplitz systems with $m\times m$ quasiseparable blocks, as well as quadratic matrix equations with $m\times m$ quasiseparable coefficients, based on cyclic reduction and…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
We study the robust matrix completion (RMC) problem subject to both sparse outliers and stochastic noise. A non-convex method termed Accelerated Robust Matrix Completion (ARMC) is proposed, which accelerates a prior non-convex approach by…
Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and…
Composed Image Retrieval (CIR) enables users to search for target images using both a reference image and manipulation text, offering substantial advantages over single-modality retrieval systems. However, existing CIR methods suffer from…
Machine learning models often suffer from catastrophic forgetting of previously learned knowledge when learning new classes. Various methods have been proposed to mitigate this issue. However, rehearsal-based learning, which retains samples…
In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming…
We study the Weighted Min Cut problem in the Adaptive Massively Parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively Parallel Computation (MPC) model. In the past…
Previous efforts on reconfigurable analog circuits mostly focused on specialized analog circuits, produced through careful co-design, or on highly reconfigurable, but relatively resource inefficient, accelerators that implement analog…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…